Tools for Teachers
Linking Assessment and Learning
“Assessment should be an
integral part of teaching.
It is the mechanism
whereby teachers can
learn how students think
about mathematics as
well as what students are
able to accomplish.”
Everybody Counts
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7th Grade Pizza Crust 2006
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7th Grade – Task 3: Pizza Crusts
Work the task and examine the rubric.
What do you think are the key mathematics the task is trying
to assess?
Look at student work in part 1a and 1b. How many of your
students are confusing
area and perimeter?
Now look at student work for 2a.
• How many of your students confused 36 sq. in. for the
perimeter instead of the area? What would their answer
have been?
• How many of your students put the length of one edge
instead of the total length of the crust?
Look at the work for designing a rectangle.
• How many of your students gave dimensions that would
yield an area different than 36 sq. inches?
• How many of your students gave dimensions that would
yield a perimeter of 36 inches?
• How many of your students gave dimensions that would
not create a rectangle?
• What other types of errors did you find?
Student G makes the common error of
confusing area and perimeter in part 2a.
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Student H draws in the units to find the perimeter in
part 2b. However, for both rectangles the area is 32
sq. in. instead of 36 square in.
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While we predict tests will measure one core standard, the tasks are rich and allow
other ideas to surface. This means that less tasks need to be used, but many
standards are covered.
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Collectively score and analyze student work
Administer high-quality
assessment tasks
TOOTHPICK SHAPES
Tom uses toothpicks to make the shapes in the
diagram below.
shape 1
6 toothpicks
shape 2
9 toothpicks
shape 3
shape 4
1. How many toothpicks make shape 3?_________________
2. Draw shape 4 next to shape 3 in the diagram
above.
5. Tom says, “I need 36 toothp icks to make shape 12.”
Tom is not correct. Explain why he is not correct.
How many toothpicks are needed to make shape 12?
Cycle of Formative
Assessment to Inform
and Improve Learning
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Leads to improved teaching
and learning in the classroom
(re-engagement lessons)
Drives the professional development
experiences of the teachers to plan
experiences focused on their students.
Document student
thinking to inform
instruction.
Opportunity to Analyze Student
Work
Design a Re-engagement Lesson
• Do the task and identify the mathematics.
• Consider how the students might approach the math. Where and
how would they be successful? What challenges or
misconceptions may arise?
• Look through the student work. Categorize solution strategies,
approaches and where students struggled. What is the story of the
task?
• Use the Tools for Teachers to compare your findings with the
history of the tasks.
MARS Task Anticipation Sheet
Task Name:__________________ Grade:____ _ Year:______ Tot Pts. _____ Core Pts._____
In anticipat ing the student work whe re wi ll students show success?
What parts of the task wil l students be
In terms of knowing and doing mathematics
successful?
what does this indicate?
In anticipat ing the student work whe re wi ll students struggle?
What parts of the task wil l students be
In terms of knowing and doing mathematics
unsuccessful?
what does this indicate? What understandings
or skill s do the students need to learn?
Conside ring strengths and weaknesses from students, wh at are plans for future teaching?
What are the im plications for future
What specifi c instruction or lesson experiences
instruction?
will you design students?
Viewing a Re-engagement Lessons
The Mathematics Assessment Collaborative uses a process of formative assessment that examines student work
and assessment results to inform instruction and design lessons to re-engage students in learning the mathematics.
Re-engagement Happens “Live”
• The heart of the process is in the discussion,
controversy, and convincing of the big
mathematical ideas.
• This is where students have the opportunity to
clarify their own thinking, confront their
misconceptions to see the errors in logic, use
mathematical vocabulary for a purpose, and
make generalizations and connections.
The design of a
Re-engagement lesson
may mirror a MARS task
Access
Core
Ramp
Re-engagement
• Makes use of actual student work - including
unique thinking, misconceptions and strategies.
• Has all students re-work a task from different
perspectives.
• Confronts misconceptions so that they can be dealt
with and let go.
• Gives some students strategies for solving
problem
• Helps other students solidify, connect, and clarify
their ideas.
Video Clip 1
Small Group
Discussions
How was the re-engagement lesson designed to provide
access?
What were the basic concepts the students needed to
learn and understand?
How were the students making sense of the
mathematics?
What did the students communicate? What did the
teachers emphasize?
Re-engagement
• Use student work and their thinking to
surface understanding and misconceptions.
• Use student work to address access into
basic concepts and foundational
understanding.
Video Clip 2
Small Group
Discussions
What is the core mathematics of the task?
What experiences in the lesson focused learning around the
core mathematics?
How was student work used to promote understanding of the
core mathematics?
Describe evidence of students demonstrating that
understanding. Where are students still struggling?
Re-engagement
• Use student work to confront common
misconceptions.
• Use student work to apply or adapt new or
unfamiliar strategies.
• Use student work to “debug” unsuccessful
approaches or flawed reasoning.
This process promotes learning core concepts.
Video Clip 3
Small Group
Discussions
Describe the components of the lesson that supported
students to work at high cognitive levels.
What aspects of the lesson encouraged students to make
connections?
How did students demonstrate deeper understanding of
the mathematical concepts?
What did the teacher do to facilitate deeper student
thinking?
Re-engagement
• Use student work to critique other students’
solutions and processes in order to deepen
understanding and ramp up the cognitive
load of the task.
Effective Formative Assessment
Strategies
• Clarifying learning intentions and sharing criteria
for success.
• Engineering effective classroom discussions.
• Providing feedback that moves learners forward.
• Activating students as the owners of their own
learning.
• Activating students as instructional resources for
one another.
Dylan Wiliam, University of London
Formative Assessment Tools
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Common Core Standards
MARS Tasks
Scoring Materials and Protocols
Tools For Teachers (Toolkits)
Student Works Analysis Tools
Re-engagement Lesson Videos
Option 1: Intensive
Implementation Strategy
Year 1:
Induction to
the Formative
Assessment
Cycle
Year 2:
Next
Generation
Assessments
Year 3:
Sustaining and
Going Deeper
Training on the
Formative Assessment
Cycle to Teams of
Teachers
4-days September
Centralized Location
conducted by MAC
Facilitators
Local
Formative
Assessment
Session
6 days for Teams
led by MAC
Facilitator
Training for Next
Generation Assessments
to Teams of Teachers
Local
Formative
Assessment
Session
4-days Aug/Sep
Centralized Location
conducted by MAC
Facilitators
6 days for Teams
led by MAC
Facilitator
Local
Formative
Assessment
Session
6 days for Teams
led by Teachers
Next
Generation
Assessments
Taught
Reengagement
lessons taught
Next
Generation
Assessments
Taught
Option 2: : Introductory Training
with Gradual Support Strategy
Year 1:
Induction to
the Formative
Assessment
Cycle
Year 2:
Next
Generation
Assessments
Training on the
Formative Assessment
Cycle to Teams of
Teachers
3-days September
Centralized Location
conducted by MAC
Facilitators
Local
Formative
Assessment
Session
3 days for Teams
led by MAC
Facilitator
Training for Next
Generation Assessments
to Teams of Teachers
Local
Formative
Assessment
Session
3-days Aug/Sep
Centralized Location
conducted by MAC
Facilitators
4 days for Teams
led by MAC
Facilitator
Next
Generation
Assessments
Taught
Option 3: Leader Training and
Indirect Support Strategy
Intensive Training for
District Math Leaders
One Year Option
For District Math
Leaders (DML)
Trainer of
Trainers Model to
Support Target
Teachers (TT)
4-days September
Centralized Location
Conducted by MAC
Follow-up Training for
District Math Leaders
2-days Oct/Nov
Centralized Location
Conducted by MAC
Follow-up Training for
District Math Leaders
2-days Jan.
Centralized Location
Conducted by MAC
Follow-up Training for
District Math Leaders
2-days Mar.
Centralized Location
Conducted by MAC
Local
Formative
Assessment
Session
1 day for TT
conducted by DML
Local
Formative
Assessment
Session
1 day for TT
conducted by DML
Local
Formative
Assessment
Session
1 day for TT
conducted by DML
Local
Formative
Assessment
Session
1 day for TT
conducted by DML